Finite Group Databasebeta

← #30599169

Subgroups — #30599169

Order 15616.

346 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461744C211yesmaximal, characteristic
2D61⋊#334C211yesmaximal, characteristic
3#21461336C212yesmaximal
4#21460688C212yesmaximal
5#21454748C211yesmaximal, characteristic
6#16840767C2212yes—
7D61⋊(C4⋊C8)C2212yes—
8#16840638—21no—
9#16840638—21no—
10#16840624—21no—
11#16840623—21no—
12#16840622—22no—
13#16840621—22no—
14#16840316C2211yescharacteristic
15#16839893C411yescharacteristic
16#16839891—21no—
17#16839889C411yescharacteristic
18C8×Dic122—21no—
19C8×Dic122C411yescharacteristic
20#16839787—21no—
21#16839784C2211yescharacteristic
22#16839716—21no—
23C4×C8×D61C2211yescharacteristic
24C8×Q8×C61C411yescharacteristic
25C2×#11758213—22no—
26C2×D61⋊C8—22no—
27#14519844—22no—
28#14519844—22no—
29#14519844—22no—
30C4⋊#92420—22no—
31C2×#11758189—21no—
32C2×C8×D61D411yescharacteristic
33C2×C8×D61D411yescharacteristic
34#14519776D411yescharacteristic
35#14519775D411yescharacteristic
36#14519767—21no—
37#14519757Q811yescharacteristic
38#14519755—21no—
39#14519753Q811yescharacteristic
40C4×Dic122—21no—
41C4×Dic122C2×C411yescharacteristic
42#14519734—21no—
43C42×D61C2311yescharacteristic
44C4⋊#92418—21no—
45C4⋊#92418C2×C411yescharacteristic
46#14519706—21no—
47#14519706—21no—
48#14519706—21no—
49#14519688—21no—
50#14519687—21no—
51C4×#92418C2×C411yescharacteristic
52C8×Dic61—21no—
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C4×Q8×C61C2×C411yescharacteristic
56C4⋊C8×C61—21no—
57C4⋊C8×C61C2×C411yescharacteristic
58C4×C8×C61—21no—
59C4×C8×C61C2×C411yescharacteristic
60C2×Q8×C61C4⋊C411yescharacteristic
61C2×C4×D61C2×D411yescharacteristic
62C2×C4×D61C2×Q811yescharacteristic
63C2×C4×D61#4111yescharacteristic
64C2×Dic122—21no—
65C2×Dic122C4⋊C411yescharacteristic
66C2×#92420—42no—
67C2×#92420—42no—
68#11758213—42no—
69#11758213—42no—
70D61⋊C8—82no—
71C2×C8×C61—21no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22⋊C411yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61C4⋊C411yescharacteristic
76C42×C61—21no—
77C42×C61C22×C411yescharacteristic
78#11758198—21no—
79#11758198—21no—
80C4⋊Dic61—21no—
81C4⋊Dic61C4⋊C411yescharacteristic
82#11758196—21no—
83#11758196—21no—
84#11758196—21no—
85#11758196—21no—
86#11758196—21no—
87C4×Dic61—21no—
88C4×Dic61C2×D411yescharacteristic
89C4×Dic61C2×D411yescharacteristic
90C4×Dic61#4111yescharacteristic
91C2×#92418—21no—
92C2×#92418C22⋊C411yescharacteristic
93C2×#92418C22⋊C411yescharacteristic
94#11758189—42no—
95C8×D61—22no—
96C8×D61—22no—
97C22×D61C22⋊Q811yescharacteristic
98Q8×C61—41no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61C2×C4⋊C411yescharacteristic
103C2×C4×C61#11711yescharacteristic
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61#12111yescharacteristic
107C2×Dic61#12111yescharacteristic
108C2×Dic61C22⋊Q811yescharacteristic
109C4×D61—22no—
110C4×D61—41no—
111C4×D61#13512yes—
112C4×D61#13712yes—
113Dic122—42no—
114Dic122—41no—
115#92420—82no—
116#92420—82no—
117C8×C61—21no—
118C8×C61—21no—
119C8×C61—41no—
120#92418—21no—
121#92418—21no—
122#92418—41no—
123#8687—611nomaximal, Sylow
124C22×C61#38011yescharacteristic
125C2×D61—21no—
126C2×D61—21no—
127C2×D61#47912yes—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61#41611yescharacteristic
133C4×C61#41911yescharacteristic
134Dic61—21no—
135Dic61—41no—
136Dic61—41no—
137Dic61#46412yes—
138Dic61#47112yes—
139#2960—611no—
140#1837—611no—
141C2×#334—611no—
142#1550—612no—
143#1292—612no—
144C2×C61#180511yescharacteristic
145C2×C61#181311yescharacteristic
146C2×C61#181511yescharacteristic
147D61—22no—
148#533—611no—
149#446—611no—
150#446—611no—
151#446—1221no—
152C8×Q8—611no—
153C8×Q8—1221no—
154C8×Q8#692311yescharacteristic
155#424—1221no—
156#423—611no—
157#423—612no—
158C2×C4⋊C8—612no—
159#405—1221no—
160C2×C4×C8—611no—
161#341—1221no—
162#341—1221no—
163#334—1221no—
164#334—1221no—
165#333—1222no—
166#332—1222no—
167C61#868711yescharacteristic, complemented, Sylow
168C2×M16—1221no—
169C2×M16—1222no—
170C22×C8—611no—
171C22×C8—611no—
172C22×C8—1222no—
173C4⋊Q8—611no—
174C4⋊Q8—611no—
175#125—1221no—
176C22⋊Q8—611no—
177C22⋊Q8—611no—
178C22⋊Q8—1221no—
179C4×Q8—611no—
180C4×Q8—1221no—
181C4×Q8C2×#692311yescharacteristic
182#117—1221no—
183C2×C42—611no—
184C4⋊C8—21no—
185C4⋊C8—611no—
186C4⋊C8—1221no—
187C4⋊C8—1221no—
188C4⋊C8—1222no—
189C4⋊C8—1222no—
190C4⋊C8—1222no—
191C4⋊C8—1222no—
192C4⋊C8—1221no—
193C4⋊C8—1221no—
194C4⋊C8C2×#692311yescharacteristic
195#97—1221no—
196#97—1221no—
197C4×C8—21no—
198C4×C8—611no—
199C4×C8—611no—
200C4×C8—611no—
201C4×C8—1221no—
202C4×C8C2×#692311yescharacteristic
203C2×Q8—611no—
204C2×Q8—1221no—
205C2×Q8C4⋊#692311yescharacteristic
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209M16—2442no—
210M16—2442no—
211M16—2442no—
212C2×C8—21no—
213C2×C8—611no—
214C2×C8—611no—
215C2×C8—1222no—
216C2×C8—1222no—
217C2×C8—1221no—
218C2×C8—4882no—
219C2×C8—2442no—
220C2×C8—2442no—
221C2×C8C22⋊#692311yescharacteristic
222C2×C8C22⋊#692311yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—611no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4C4⋊#692311yescharacteristic
232C22⋊C4—1221no—
233C22⋊C4—1221no—
234C42—21no—
235C42—611no—
236C42—611no—
237C42—611no—
238C42—1221no—
239C42C22×#692311yescharacteristic
240C23—611no—
241Q8—41no—
242Q8—2441no—
243Q8—2442no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—612no—
249C2×C4—612no—
250C2×C4—611no—
251C2×C4—1222no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—2441no—
255C2×C4C2×C22⋊#692311yescharacteristic
256C2×C4C2×C4⋊#692311yescharacteristic
257C2×C4#1451985611yescharacteristic
258C8—21no—
259C8—21no—
260C8—41no—
261C8—1221no—
262C8—1221no—
263C8—4882no—
264C8—4882no—
265C8—2441no—
266C22—612no—
267C22—1221no—
268C22—1221no—
269C22#1684070411yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—612no—
275C4—612no—
276C4—1221no—
277C4—2441no—
278C4—2441no—
279C4#1684075211yescharacteristic
280C4#1684075511yescharacteristic
281C2—1222no—
282C2#2146169011yescharacteristic
283C2#2146170311yescharacteristic
284C2#2146170711yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC8×Q8×C61C4
socleC22×C61#380
prime radicalC22×D61C22⋊Q8
cosocleC42×D61C23
hypercenterC8×Q8#6923
hypocenterC61#8687
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
167. C61#8687semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214617442
D61⋊#3342
#214613362
#214606882
#214547482
#868761